2x^2-32x-192=0

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Solution for 2x^2-32x-192=0 equation: 


Simplifying
2x2 + -32x + -192 = 0

Reorder the terms:
-192 + -32x + 2x2 = 0

Solving
-192 + -32x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-96 + -16x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-96 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
-96 + -16x + x2 = 0

Solving
-96 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + -16x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + -16x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + -16x + x2 = 0 + 96
-16x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
-16x + x2 = 96

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 96 + 64

Reorder the terms:
64 + -16x + x2 = 96 + 64

Combine like terms: 96 + 64 = 160
64 + -16x + x2 = 160

Factor a perfect square on the left side:
(x + -8)(x + -8) = 160

Calculate the square root of the right side: 12.649110641

Break this problem into two subproblems by setting 
(x + -8) equal to 12.649110641 and -12.649110641.


Subproblem 1
x + -8 = 12.649110641

Simplifying
x + -8 = 12.649110641

Reorder the terms:
-8 + x = 12.649110641

Solving
-8 + x = 12.649110641

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + x = 12.649110641 + 8

Combine like terms: -8 + 8 = 0
0 + x = 12.649110641 + 8
x = 12.649110641 + 8

Combine like terms: 12.649110641 + 8 = 20.649110641
x = 20.649110641

Simplifying
x = 20.649110641


Subproblem 2
x + -8 = -12.649110641

Simplifying
x + -8 = -12.649110641

Reorder the terms:
-8 + x = -12.649110641

Solving
-8 + x = -12.649110641

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + x = -12.649110641 + 8

Combine like terms: -8 + 8 = 0
0 + x = -12.649110641 + 8
x = -12.649110641 + 8

Combine like terms: -12.649110641 + 8 = -4.649110641
x = -4.649110641

Simplifying
x = -4.649110641


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.649110641, -4.649110641}
Solution
x = {20.649110641, -4.649110641}

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